The　coordinated　motion　control　and　flexible　vibration　suppression　problems　of　flexible　space　manipulator　are　studied.　With　the　assumed　mode　method　and　the　linear　momentum　conservation　of　the　system,　the　system　dynamics　model　of　the　space　manipulator　is　derived.　Based　on　the　hybrid　sliding　mode　concept,　an　adaptive　variable　structure　control　scheme　is　proposed　for　the　flexible　space　manipulator　to　achieve　the　coordinated　motion　between　the　base＇s　attitude　and　the　arm＇s　joints,　which　accounts　for　the　uncertainty　in　inertial　parameters.　The　hybrid　sliding　mode　introduced　consists　of　two　parts,　the　frequency　shaped　optimal　sliding　mode　and　the　terminal　sliding　mode.　The　former　is　used　to　suppress　the　vibration　of　flexible　link　of　the　system,　and　the　latter　is　utilized　to　guarantee　the　convergence　of　system　tracking　errors　in　finite　time.　Moreover,　the　control　scheme　proposed　does　not　require　the　foreknowledge　of　flexible　variables　in　control.　Thus,　it　can　effectively　avoid　the　real-time　measurements　and　feedbacks　of　system　flexible　variables,　and　be　more　suitable　for　practical　applications.　Simulation　results　demonstrate　the　effectiveness　of　the　proposed　control　scheme.